A cascade decomposition of weighted finite transition systems

Abstract

We consider weighted finite transition systems with weights from naturally ordered semirings. Such semirings comprise distributive lattices as well as the natural numbers with ordinary addition and multiplication, and the max -plus-semiring. For these systems we explore the concepts of covering and cascade product. We show a cascade decomposition result for such weighted finite transition systems using special partitions of the state set of the system. This extends a classical result of automata theory to the weighted setting.